Graphs and their Applications

Course guarantor:

Lecturer:

Jiří Demel

Tutor:

Supervisor:

Department of Applied Informatics

Synopsis:

Fundamentals of graph theory. Emphasis is laid on basic concepts, applications and algorithms. From the contents: connectivity, strong conectivity, trees, shortest

paths, flows in networks, Eulerian and Hamiltonian

paths, colorings, independent sets, planar graphs.

Requirements:

no prerequisities

Syllabus of lectures:

Basic notions (graphs, vertices, edges, degrees, paths, cycles, etc.).

Applications of path problems.

Searching algorithms (labeling, breath first search, depth first search).

Notions based on undirected paths (connected components, trees, minimal spanning trees).

Notions based on directed paths (strongly connected components, topological sorting, rooted trees, transitive closure).

Shortest path.

Problems related to shortest paths.

Flows in networks.

Application of network flow problems.

Matchings, Assignment problem.

Eulerian graphs, Chinese postman problem.

Hamiltonian paths and cycles. Travelling salesman problem.

Colorings, independent sets and cliques.

Planar graphs.

Syllabus of tutorials:

Basic notions (graphs, vertices, edges, degrees, paths, cycles, etc.).

Applications of path problems.

Searching algorithms (labeling, breath first search, depth first search).

Notions based on undirected paths (connected components, trees, minimal spanning trees).

Notions based on directed paths (strongly connected components, topological sorting, rooted trees, transitive closure).

Shortest path.

Problems related to shortest paths.

Flows in networks.

Application of network flow problems.

Matchings, Assignment problem.

Eulerian graphs, Chinese postman problem.

Hamiltonian paths and cycles. Travelling salesman problem.

Colorings, independent sets and cliques.

Planar graphs.

Study Objective:

Ability to use the graph as means of expression to model real situations, ability to solve basic graph problems.

Study materials:

Diestel, R.: Graph Theory, Springer, 1996,

Swamy, M., N., S., Thulasiraman, K., Graphs, Networks and Algorithms. New York, John Wiley&Sons, Inc., 1981.

Demel, J.: Graphs and their Applications, (internal material).

Note:

Time-table for winter semester 2024/2025:

Time-table is not available yet

Time-table for summer semester 2024/2025:

Time-table is not available yet

The course is a part of the following study plans: